US6914442B2 - Method for measuring resistivity of semiconductor wafer - Google Patents
Method for measuring resistivity of semiconductor wafer Download PDFInfo
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- US6914442B2 US6914442B2 US10/423,885 US42388503A US6914442B2 US 6914442 B2 US6914442 B2 US 6914442B2 US 42388503 A US42388503 A US 42388503A US 6914442 B2 US6914442 B2 US 6914442B2
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/26—Testing of individual semiconductor devices
- G01R31/2648—Characterising semiconductor materials
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- the present invention relates to a method for measuring resistivity of a semiconductor wafer (hereinafter, in some cases, referred to as a wafer) by the use of surface photo voltage method.
- SPV surface photo voltage
- reference numeral 10 denotes a device for measuring the SPV.
- a light emitting diode 12 (hereinafter, referred to as an LED) is usually used as its light source because it is intermittently chopped with ease.
- Light 12 a of the LED 12 chopped at an appropriate frequency is converged through an aperture 14 and a lens 16 and applied to the surface of an Si wafer W.
- Reference numeral 18 denotes an LED driver that drives the LED 12 and is connected to a lock-in amplifier 20 .
- the AC-SPV is measured by the lock-in amplifier 20 synchronized with a driving frequency of the LED connected to a transparent electrode 24 placed on the Si wafer W with a Mylar film 22 interposed between them.
- the Mylar film 22 is not necessarily provided but the AC-SPV can be also measured by the transparent electrode 24 placed on the surface of the Si wafer W via an air gap of about from several tens ⁇ m to 200 ⁇ m.
- the transparent electrode 24 can be formed, for example, by evaporating indium oxide on a glass substrate.
- reference numeral 26 denotes a glass plate placed on the upper surface of the transparent electrode 24 and reference numeral 28 denotes a metal electrode, respectively.
- FIG. 5 the principle of measuring resistivity of the wafer is shown in FIG. 5 .
- the positive charge Qs Qs>0
- free holes near the surface of a bulk are electrostatically repulsed by the positive charge thereby to be pressed into the bulk.
- the negative charge Qsc Qsc ⁇ 0
- a region where the free holes are not present, that is, a depletion layer region 36 is formed near the surface of the bulk.
- An inner electric field is formed in this depletion layer region 36 by the positive charge Qs on the surface and the negative charge Qsc in the Si bulk.
- a transparent electrode 30 for measuring the AC-SPV is placed on the Si wafer W via an air gap 32 of 100 ⁇ m in thickness. This construction enables advantageously to measure the AC-SPV in a manner of noncontact with the surface of the Si wafer.
- Light having a wavelength shorter than a wavelength corresponding to an energy gap of Si is used as incident light 34 a [chopped intermittent light of 40 KHz to 50 KHz] from a light source 34 . The reason why light having such a short wavelength is used is given as follows.
- the depletion layer 36 formed near the surface of the Si wafer W is 1 ⁇ m, all of the incident light is absorbed in the depletion layer 36 . As a result, excessive carriers excited in the Si wafer by the incident light are generated only in the depletion layer 36 .
- the AC-SPV can be expressed by the following equation (for example, Emil Kamieniecki et al, J. Appl. Phys. Vol. 54 (11), November 1983, p. 6481).
- ⁇ V s ⁇ j ⁇ ⁇ 1 (1 ⁇ R ) q C dp ⁇ 1 (2)
- V s is the electric potential barrier height of the surface
- q is the elementary quantity of the electric charge
- C dp is the capacitance of the depletion layer formed on the surface of the specimen
- R is the optical reflection factor
- ⁇ is the incident photon flux.
- ⁇ V s is a change in V s that is observed as AC-SPV in the transparent electrode 30 placed on the specimen in FIG. 5 via the air gap 32 of about 100 ⁇ m in thickness.
- reference numeral 38 denotes a ground electrode.
- FIG. 6 The general dependence of the AC-SPV on a modulation frequency measured under conditions in which excessive carriers are generated only in the depletion layer 36 in this manner is shown in FIG. 6 .
- some people try to use an equivalent circuit.
- R. S. Nakhmason, et al., Solid-St. Electron, 18 (1975), pp. 627-634, and C. Munakata et al., Jpn. J. A. P. 23, (1984), pp. 1451-1460 are mentioned.
- An equivalent circuit in the case where a strong inversion layer is formed on the surface of the semiconductor, which is proposed by C. Munakata et al. is shown as one example in FIG. 7 . It is generally known that the respective states of a neutral state, a depletion state, a weak inversion state, and a strong inversion state can be produced on the surface of the semiconductor by the use of surface treatment.
- V s is the electric potential barrier height
- J ph is the photoelectric current
- Z is the impedance
- the equivalent circuit is a parallel circuit of the capacitance and the resistance. Therefore, the SPV limited by the conductance g in and g dp appears in a region where the modulation frequency of the incident light is low. It is understood that the SPV takes a constant value, irrespective of the modulation frequency, in this region (a region “A” in FIG. 6 , which is hereinafter referred to as a low frequency region).
- a region where the modulation frequency is high (a region “B” in FIG. 6 , which is hereinafter referred to as a high frequency region)
- the observed SPV signal is inversely proportional to the modulation frequency f because the AC-SPV is limited by the capacitance C in and C dp .
- An intermediate region of the modulation frequency between both of the regions (a region “C” in FIG. 6 , which is hereinafter referred to as a transition frequency region) is a transition region from the region limited by the conductance to the region limited by the capacitance.
- ⁇ s is the relative dielectric constant of Si.
- the depletion layer capacitance C dp of the object to be measured (Si) can be calculated from the equation (2). Further, from the equation (5), the depletion layer width W d can be calculated. If the surface of the object to be measured is in the strong inversion state, the depletion layer width W d becomes a maximum value W max and can be expressed by the following equation.
- W max ⁇ square root over (4 ⁇ s kT ln( N sc /n i )/( q 2 N sc )) ⁇ square root over (4 ⁇ s kT ln( N sc /n i )/( q 2 N sc )) ⁇ (6)
- W max is the maximum depletion layer width in the strong inversion state
- ⁇ s is the relative dielectric constant of Si
- k is the Boltzmann constant
- N sc is the dopant concentration
- n i is the intrinsic carrier density of Si
- q is the elementary quantity of the electric charge, respectively.
- the dopant concentration of the object to be measured can be calculated by the use of this equation.
- a commercially available device for measuring resistivity of an Si wafer by the use of the AC-SPV for example, a resistivity measuring device commercially sold by QC Solutions, Inc. (under a trade name of “SCP”) uses light with a wavelength of 450 nm that is chopped (at a chopping frequency of 40 kHz) as incident light.
- SCP QC Solutions, Inc.
- the device can measure the depletion layer capacitance.
- the Si wafer is subjected to treatment called ROST (Rapid Optical Surface Treatment) as pretreatment before measurement.
- ROST Rapid Optical Surface Treatment
- the Si wafer is rapidly heated at a temperature of about 300° C. for about 30 seconds by a halogen lamp. It is assumed that the positive charge is generated on the surface of the specimen by this pretreatment to bring the surface into the strong inversion state.
- the dopant concentration of the object to be measured can be calculated from C dp .
- the dopant concentration can be converted to resistivity according to ASTM (F723-81). As a result, resistivity can be calculated in principle.
- a method for bringing the surface of the specimen into the strong inversion state can be considered.
- the p-type Si wafer it is enough that a considerable amount of the positive charge is generated on the surface of the Si wafer.
- Specific methods for generating the positive charge on the surface of the Si wafer include not only the above-mentioned ROST but also (1) dipping of the wafer in an HF water solution (C. Munakata, Semicond. Sci. Technol., 5 (1990), pp. 842-846, and (2) thermally oxidizing of the wafer (B. E. Deal, IEEE Trans. Electron Device, ED-27, (1980), pp. 606-608 and others).
- the positive charge is generated but the surface of the wafer is not brought into the strong inversion state either.
- the method ( 2 ) in a region where resistivity is comparatively high, the surface of the wafer is brought into the strong inversion state but thermal oxidization is required, thereby inspection cost being increased.
- the dopant concentration of the interface between the substrate and an epitaxial layer is varied by the heat treatment.
- the other methods also present the following problems: the strong inversion state cannot be obtained and the wafer is stained by the treatment, so that the measured wafer cannot be shipped as a product wafer as it is. As a result, the present inventor came to recognize that it was difficult to produce the strong inversion state without degrading the quality of the Si wafer.
- the present invention has been made in view of these problems. It is the object of the present invention to provide a method for measuring resistivity by the use of an AC-SPV method even in a depletion state or a weak inversion state.
- a method for measuring resistivity of a semiconductor wafer in accordance with the present invention is a method for measuring resistivity of a semiconductor wafer by the use of a surface photo voltage method, and comprises the steps of: (a) measuring a surface photo voltage value in both regions of a low frequency region in which a constant surface photo voltage value is obtained irrespective of a frequency of incident light on a semiconductor wafer to be measured and a high frequency region in which the surface photo voltage value inversely proportional to the frequency of the incident light is obtained and calculating a cut-off frequency f c from the obtained measured value; (b) calculating a depletion layer width W d from capacitance C dp calculated from the surface photo voltage value in the high frequency region; (c) calculating majority carrier conductance g mj from the cut-off frequency f c and the capacitance C dp ; and (d) calculating surface potential U s and Fermi potential U F from the cut-off frequency f
- the present invention is a nondestructive method for measuring resistivity, characterized in that in the AC-SPV method, an AC-SPV signal is measured in at least two regions of a low modulation frequency region in which the AC-SPV is limited by conductance and a high modulation frequency region in which the AC-SPV is limited by capacitance.
- FIG. 8 and FIG. 9 show the measurement results of resistivity of an epitaxial wafer having a p/p + structure (an epitaxial wafer in which a p-type epitaxial layer having ordinary resistivity is formed on a p-type substrate having low resistivity) by the use of resistivity measuring device (under the trade name of “SCP”) commercially sold by the above-mentioned QC Solution Corp.
- Resistivity of the epitaxial layer of the epitaxial wafer used for the measurement was about 10 ⁇ cm. This was confirmed by a Schottky CV method that is currently widely used.
- the thickness of the epitaxial layer was about 10 ⁇ m.
- FIG. 8 shows calculation results of the dopant concentration of the epitaxial layer obtained by once subjecting the specimen to the ROST before measurement and then by repeatedly measuring the AC-SPV.
- the abscissa shows the number of measurement and one measurement took about one minute.
- the dopant concentration of the epitaxial layer decreases with time and measured values vary with time.
- FIG. 9 shows the results in the case where the ROST and the AC-SPV measurement were repeatedly performed for the specimen.
- the abscissa shows the number of measurement, as is in FIG. 8 . Since the specimen was each time subjected to the ROST and then measured, one measurement took about two minutes. In this case, the dopant concentration increases as the number of measurement increases, which shows that the measurement could not be stably performed.
- the present inventor evaluated the surface potential U s (physical quantity by dividing surface potential ⁇ s (v) by thermal voltage kT/q, where k is the Boltzmann constant, T is the absolute temperature, and q is the elementary quantity of the electric charge) of no unit of a wafer subjected to the ROST, for example, by a method proposed by Munakata et al. (Jpn. J. A. P., Vol. 26, No. 2, February 1987, pp.
- the surface potential U s always varies owing to the adhesion of moisture to the surface of the Si wafer, the formation of a natural oxide film, and the like.
- the following table 1 shows the measurement results of the surface potential U s of no unit just after subjecting the above-mentioned specimen to the ROST and after a lapse of 5 hours thereafter.
- the measured surface potential U s is less than 23.1 in both cases, so that it is found that the surface of the Si wafer was not brought into the strong inversion state, but only into the depletion state or the weak inversion state.
- the measured surface potential U s after a lapse of 5 hours is smaller than that just after the ROST, which leads to understanding that the surface potential has decreased or varied with time.
- the present inventor was confident that the fundamental reason why the measurement result of resistivity (dopant concentration) by the SPV method was not stable lies in calculating the resistivity on the assumption that in spite of the fact that the surface was not brought into the strong inversion state by the ROST but only into the depletion state or the weak inversion state, the surface was brought into the strong inversion state. Then, the present inventor has conducted a diligent study on a measuring method by which resistivity (dopant concentration) can be correctly calculated even though the surface of the wafer to be measured is not in the strong inversion state but in the depletion state or the weak inversion state, and has come to complete the present invention.
- FIG. 1 is a flow chart showing the order of processes of a method for measuring resistivity of a semiconductor wafer of the present invention
- FIG. 2 is a conceptual view showing a method for finding a cut-off frequency fc in the method of the present invention
- FIG. 3 is an illustration showing an equivalent circuit of an AC-SPV signal in the case where the surface of a semiconductor is in a depletion state or a weak inversion state;
- FIG. 4 is an illustration showing one example of a device for measuring SPV
- FIG. 5 is an illustration showing the principle of measuring resistivity of a p-type Si wafer
- FIG. 6 is a graph showing an AC-SPV signal
- FIG. 7 is an illustration showing an equivalent circuit in the case where a strong inversion layer is formed on the surface of a semiconductor
- FIG. 8 is a graph showing results of measurement (one ROST+repetitive measurement of AC-SPV) of resistivity of an epitaxial wafer having a p/p + structure.
- FIG. 9 is a graph showing results of measurement (repetitive measurement of ROST+AC-SPV) of resistivity of an epitaxial wafer having a p/p + structure.
- FIG. 1 is a flow chart showing the order of processes of a method for measuring resistivity (dopant concentration) of a semiconductor wafer in accordance with the present invention.
- a wafer to be measured is set on a measuring device using an SPV method and SPV is measured in respective regions of a low frequency region and a high frequency region by varying the modulation frequency of incident light. Since the SPV in the low frequency region is constant and the SPV in the high frequency region is inversely proportional to the frequency, if the SPV is measured at least one point (one frequency) in each of the regions, a cut-off frequency can be determined at the next step.
- the SPV at a plurality of points it is also possible to measure the SPV at a plurality of points by the use of a plurality of frequencies in each of the regions. It is recommended that the frequency of from 0.1 Hz to 1000 Hz is selected in the low frequency region and the frequency of from 0.5 kHz to 500 kHz is selected in the high frequency region, provided that the frequency is to be selected in a condition of the low frequency ⁇ the higher frequency. From the measurement results of the SPV in the high frequency region, depletion layer capacitance C dp formed on the surface of the wafer can be also calculated and a depletion layer width W d can be obtained from the value of C dp by the use of the above-mentioned equation (5).
- the cut-off frequency f c is found.
- the cut-off frequency f c is the frequency at the intersect of the extrapolated lines of the SPVs measured each in the low frequency region and the high frequency region.
- FIG. 2 is shown a conceptual view of a method for finding the cut-off frequency f c . As shown in FIG.
- majority carrier conductance g mj is calculated from the depletion layer capacitance C dp found at the step 100 and the cut-off frequency f c found at the step 102 .
- a detailed calculation method is as follows.
- FIG. 3 is shown the equivalent circuit of an AC-SPV signal in the case where the surface of the semiconductor is in a depletion state or a weak inversion state, which is proposed by C. Munakata et al. (J. J. A. P, 26, (1987), pp. 226-230).
- C it is the interface capture capacitance
- g it is the interface capture conductance
- C dp is the depletion layer capacitance
- g mj is the majority carrier conductance.
- their detailed descriptions will be omitted because they are not the essence of the present invention.
- the depletion capacitance C dp , the cut-off frequency fc, and the majority carrier conductance g mj in the depletion state/the weak inversion state can be easily measured/calculated by the above-mentioned steps 100 to 104 by the use of the AC-SPV method. Then, it is known that the following relations are established between these parameters, for example, in the case of a p-type semiconductor.
- p s is the hole density in the surface of the wafer
- ⁇ p is the hole mobility
- U s is the surface potential
- U F is the Fermi potential
- L Di is the intrinsic device length
- p po is the hole density in the p-type Si bulk
- k is the Boltzmann constant
- T is the absolute temperature
- q is the elementary quantity of the electric charge
- V pdm is the hole maximum saturation velocity
- W d is the depletion layer width, respectively.
- the cut-off frequency f c , the capacitance C dp , the depletion layer width W d , and the majority carrier conductance g mj which are already obtained, are substituted into the equation (17) from the equation (10) to solve the simultaneous equations, thereby the surface potential U s and the Fermi potential U F being calculated (step 108 ). If the Fermi potential U F is found, it is possible to calculate the dopant concentration from the known relationship between the Fermi potential and the dopant concentration (for example, “Semiconductor and Device (I)” written by Takuo Sugano, p. 319, published by Syoukoudou) and then to convert the dopant concentration into resistivity (step 110 ).
- the known relationship between the Fermi potential and the dopant concentration for example, “Semiconductor and Device (I)” written by Takuo Sugano, p. 319, published by Syoukoudou
- Resistivity (dopant concentration) of an epitaxial wafer having an epitaxial layer (thickness: 3 ⁇ m) with a p-type of conductivity and unknown resistivity was measured by the measuring method of the present invention in the following manner.
- the epitaxial wafer just after epitaxial growth was placed on an SPV measuring device and subjected to ROST and then SPV was measured in a low frequency region and a high frequency region.
- the frequencies of an incident light in the low frequency region and the high frequency region were 10 Hz and 50 kHz, respectively.
- the cut-off frequency fc of 3.31 kHz was obtained.
- the depletion layer capacitance C dp of 6.19 nF was obtained and hence the depletion layer width W d of 1.67 ⁇ m was calculated from the equation (5).
- the surface potential was changed with the passage of time due to the effect of the left time. As a result, the measured values were different from those obtained last time, but the obtained Fermi potential U F was the same value of 0.25 as that obtained last time. More specifically, it was found that although the surface potential was changed with the passage of time, the intrinsic dopant concentration (1.5 ⁇ 10 15 /cm 3 ) of the epitaxial layer could be measured.
Abstract
Description
J ph =qΦ(1−R) (1)
δV s =−jδφω −1(1−R)q C dp −1 (2)
δV s =δJ ph |Z| (3)
Z=1/(g in +g dp +jω(C in +C dp)) (4)
C dp=∈s /W d (5)
W max=√{square root over (4∈s kT ln(N sc /n i)/(q 2 N sc))}{square root over (4∈s kT ln(N sc /n i)/(q 2 N sc))} (6)
TABLE 1 | |||
Just after ROST | After a lapse of 5 hours after ROST | ||
Us = 15.9 | Us = 15.4 | ||
δV s =δJ ph |Z| (3)
Z=1/(g it +g mj +jω(C it +C dp)) (7)
Z=1/(g mj +jωC dp) (8)
fc=(1/2π)×(g mj /C dp) (9)
F(U s, UF)=√{square root over (2)}√{square root over ((cosh(U S−UF)+U Ssin hU F−cosh UF))} (12)
E s=√{square root over (2(U S−1))}/(βL De) (13)
β=q/kT (14)
E 0 =v pdm/μp (15)
L De =L Di/√{square root over ((expU F))} (16)
W d =L Di/√{square root over ((2|U S|exp(−|U F|)))} (17)
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JP2001379103A JP3736749B2 (en) | 2001-12-12 | 2001-12-12 | Method for measuring resistivity of semiconductor wafer |
US10/423,885 US6914442B2 (en) | 2001-12-12 | 2003-04-28 | Method for measuring resistivity of semiconductor wafer |
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Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
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US20070152699A1 (en) * | 2005-12-29 | 2007-07-05 | Dongbu Electronics Co., Ltd. | System and method for automatically measuring carrier density distribution by using capacitance-voltage characteristics of a MOS transistor device |
US20080108155A1 (en) * | 2005-03-25 | 2008-05-08 | Shin-Etsu Handotai Co., Ltd. | Method For Evaluating Dopant Contamination Of Semiconductor Wafer |
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JP2008241642A (en) * | 2007-03-29 | 2008-10-09 | Dainippon Screen Mfg Co Ltd | Surface electrometer |
CN105242189B (en) * | 2015-10-13 | 2018-10-19 | 中国人民解放军海军工程大学 | IGBT health status monitoring methods based on collection emitter-base bandgap grading saturation voltage drop and solder layer voidage |
CN115346889A (en) * | 2022-10-17 | 2022-11-15 | 广州粤芯半导体技术有限公司 | Monitoring method of epitaxial process |
Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4051437A (en) * | 1976-04-02 | 1977-09-27 | The United States Of America As Represented By The Secretary Of The Navy | Method and apparatus for semiconductor profiling using an optical probe |
US5140272A (en) * | 1987-09-25 | 1992-08-18 | Hitachi, Ltd. | Method of semiconductor surface measurment and an apparatus for realizing the same |
-
2001
- 2001-12-12 JP JP2001379103A patent/JP3736749B2/en not_active Expired - Fee Related
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Patent Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4051437A (en) * | 1976-04-02 | 1977-09-27 | The United States Of America As Represented By The Secretary Of The Navy | Method and apparatus for semiconductor profiling using an optical probe |
US5140272A (en) * | 1987-09-25 | 1992-08-18 | Hitachi, Ltd. | Method of semiconductor surface measurment and an apparatus for realizing the same |
Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20080108155A1 (en) * | 2005-03-25 | 2008-05-08 | Shin-Etsu Handotai Co., Ltd. | Method For Evaluating Dopant Contamination Of Semiconductor Wafer |
US7622312B2 (en) * | 2005-03-25 | 2009-11-24 | Shin-Etsu Handotai Co., Ltd. | Method for evaluating dopant contamination of semiconductor wafer |
US20070152699A1 (en) * | 2005-12-29 | 2007-07-05 | Dongbu Electronics Co., Ltd. | System and method for automatically measuring carrier density distribution by using capacitance-voltage characteristics of a MOS transistor device |
US7489157B2 (en) * | 2005-12-29 | 2009-02-10 | Dongbu Electronics Co., Ltd. | System and method for automatically measuring carrier density distribution by using capacitance-voltage characteristics of a MOS transistor device |
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JP3736749B2 (en) | 2006-01-18 |
US20040212377A1 (en) | 2004-10-28 |
JP2003179114A (en) | 2003-06-27 |
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